Aptitude - Problems on Numbers - Discussion

Let the ten's and unit digit be x and 8/x because on multiplying x*8/x we get 8. That's what is actually said at the first line of the question.

Now, suppose let's unit digit be 8/x and ten's digit be x. Now, the number becomes 10 * x + 8/x (let us consider this equation as equation number 1)

According to the question, given that
10 * x + 8/x + 18 = 10 * 8/x + x.

Further Solving by taking L.C.M on both sides we get the statement a 10x^2+8+18x = 80+x^2 (the sign (^) here denotes square of that number).

9x^2 +18x-72=0.

Take 9 as common from above equation, you'll get,
x^2 +2x-8 = 0.
x^2+4x-2x-8 = 0.
x(x+4)-2(x+4) = 0.
(x+4)(x-2) = 0.

Hence
x = 2 (since x = -4 cannot be taken becoz the digit is negative).

Now put x=2 in above equation number 1

Thus 10*x+8/x becomes
=10*2+8/2 (since x=2)
=20+4
=24
Hence the required answer is 24...
Any doubt plz ask ....!!

First let us consider the the number is xy.
Then the number value = 10x+y.

Given that if we add 18 to the number then it would be equal to reverse of the number(yx which value is 10y+x).
i.e 10x+y+18 = 10y+x.
10x+y+18-10y-x = 0.
9x-9y+18 = 0.
x-y+2 = 0 ------------------------------------------------- (1).

But we know product of digits is 8 i.e xy = 8.
then x = 8/y.

so substitute x = 8/y in equation 1.

then 8/y -y + 2 = 0.
i.e 8-y^2+2y = 0.
y^2-2y-8 = 0.

y^2 - 4y-2y -8 = 0.

y(y-4)+2(y-4) = 0.
y= -2 or 4.

we take positive y, then y= 4.
then x= 8/y = 8/4 = 2.

So the number is xy i.e 24.

First we have to check with the options then only we find answer easily.

Here the first condition is that the multiple of that two digit number is 8.
Then we check all the options. Given four options satisfying the 1st condition.

Now go to 2nd condition, i.e if 18 is added to that two digit number the answer will be reversed.
So we can check through all the options then we get 24 is the correct option.

i.e 2*4 = 8.
24 + 18 = 42.

Hence the 2 conditions are satisfied.

Two digits=x & y so two digit no = 10x+y.
Product of digits is x*y = 8.

So (10x+y)+18 = 10y+x.
i.e x-y = -2......(1).
as x*y=8 so x = 8/y.

Hence equation (1) becomes 8/y-y = -2......(2).
Solving equation(2) we get y = 2.

Putting y=2 in equation (1) we get x = 4.
So the two digited number xy = 42.

So please tell me how answer comes to 24.
Please correct me if I am wrong?

Let's not look into the options to solve this. Let's solve from the scratch--
The product of 2 digits is 8:-

1 * 8 = 8
2 * 4 = 8
4 * 2 = 8
8 * 1= 8.

So, the number has to be any of the above-given numbers i.e 18 or 24 or 42 or 81.

Now, add 18 to all the above 4 numbers, only 24 will be reversed after adding 18. => 24 = 42 (reversed).

So, 24 is the answer.

Two digits let be x and y

So, two digit no. =10x+y.
Given, xy=8.
=>y=8/x or x=8/y...(1).

So, (10x+y) +18=10y+x
=>9x+18=9y
=>x+2=y----(2).

Putting the Value of x from eqn 1 in eqn 2.
8/y-y = -2.
y^2-2y-8 = 0.
y^2-4y+2y-8 = 0.
y(y-4) +2(y-4) = 0.

y = 4/-2, y can't be a negative integer.
So y = 4.
And x = 2.
So, no. is 24.

Well the solution is such that;

Given condition:

xy = 8.
xy*18 = yx.

Now, let tens place be x and ones place be 8/x (using 1st condition).
Using second condition we will have;
10x+8/x+18=80/x+x.
Calculating we get;
x=2 and y=4.

Hence, combining we have and 2,4 i.e,24.

@Vijay.

Its very simple.

See the no 9 is divisible by only 3 (other than 1 & itself not to be considered).

So to make 7*5462 divisible by 9, * must be 0 or 3.

Trying with 0 fails to give the ans so then try with 3 it gives u the correct answer.

Possibilities of getting a product 8 is 24 or 42.
If 18 is added to 42, it gives 60 --> the reversing condition is not met.
Else if you add 18 to 24 --> 18+24 = 42, the reverse of 24.
Hence the answer is 24.

xy = 8
10x + y + 18 = 10y = x
9x - 9y + 18 = 0
x-y = -2
8/y - y = -2
So by solving above equation we get y = 4,
by putting y=4 in xy=8 so we get x = 2.
So the original no. is 10x+y = 24.